Streamwise Vorticity in the Wake of a Sliding Bubble

In many practical situations, bubbles are dispersed in a
liquid phase. Understanding these complex bubbly flows is therefore
a key issue for applications such as shell and tube heat exchangers,
mineral flotation and oxidation in water treatment. Although a large
body of work exists for bubbles rising in an unbounded medium,
that of bubbles rising in constricted geometries has received less
attention. The particular case of a bubble sliding underneath an
inclined surface is common to two-phase flow systems. The current
study intends to expand this knowledge by performing experiments
to quantify the streamwise flow structures associated with a single
sliding air bubble under an inclined surface in quiescent water. This
is achieved by means of two-dimensional, two-component particle
image velocimetry (PIV), performed with a continuous wave laser
and high-speed camera. PIV vorticity fields obtained in a plane
perpendicular to the sliding surface show that there is significant bulk
fluid motion away from the surface. The associated momentum of the
bubble means that this wake motion persists for a significant time
before viscous dissipation. The magnitude and direction of the flow
structures in the streamwise measurement plane are found to depend
on the point on its path through which the bubble enters the plane.
This entry point, represented by a phase angle, affects the nature and
strength of the vortical structures. This study reconstructs the vorticity
field in the wake of the bubble, converting the field at different
instances in time to slices of a large-scale wake structure. This is, in
essence, Taylor’s ”frozen turbulence” hypothesis. Applying this to the
vorticity fields provides a pseudo three-dimensional representation
from 2-D data, allowing for a more intuitive understanding of the
bubble wake. This study provides insights into the complex dynamics
of a situation common to many engineering applications, particularly
shell and tube heat exchangers in the nucleate boiling regime.

Authors:

• R. O’Reilly Meehan
• D. B. Murray

Keywords:

• Bubbly flow
• particle image velocimetry
• two-phase flow
• wake structures.

References:

[1] L. Fan and K. Tsuchiya, Bubble wake dynamics in liquids and
liquid-solid suspensions. Butterworth-Heinemann Stoneham, 1990.
[2] D. Bhaga and M. Weber, “Bubbles in viscous liquids: shapes, wakes
and velocities,” Journal of Fluid Mechanics, vol. 105, no. 1, pp. 61–85,
1981.
[3] R. Clift, Bubbles, drops, and particles. DoverPublications.com, accessed
06/09/13, 2005.
[4] C. Br¨ucker, “Structure and dynamics of the wake of bubbles and its
relevance for bubble interaction,” Physics of Fluids, vol. 11, p. 1781,
1999.
[5] R. Adrian and Z. Liu, “Observation of vortex packets in direct numerical
simulation of fully turbulent channel flow,” Journal of Visualization,
vol. 5, no. 1, pp. 9–19, 2002.
[6] M. Acarlar and C. Smith, “A study of hairpin vortices in a laminar
boundary,” Journal of Fluid Mechanics, vol. 175, pp. 1–83, 1987.
[7] B. Stewart, M. Thompson, T. Leweke, and K. Hourigan, “Numerical
and experimental studies of the rolling sphere wake,” Journal of Fluid
Mechanics, vol. 643, no. 1, pp. 137–162, 2010. [8] R. Zenit and J. Magnaudet, “Measurements of the streamwise vorticity in
the wake of an oscillating bubble,” International Journal of Multiphase
Flow, vol. 35, no. 2, pp. 195–203, 2009.
[9] T. Maxworthy, “Bubble rise under an inclined plate,” Journal of Fluid
Mechanics, vol. 229, pp. 659–674, 1991.
[10] A. Peron, L. Kiss, and S. Poncs´ak, “An experimental investigation of the
motion of single bubbles under a slightly inclined surface,” International
Journal of Multiphase Flow, vol. 32, no. 5, pp. 606–622, 2006.
[11] B. Podvin, S. Khoja, F. Moraga, and D. Attinger, “Model and
experimental visualizations of the interaction of a bubble with
an inclined wall,” Chemical Engineering Science, vol. 63, no. 7,
pp. 1914–1928, 2008.
[12] B. Donnelly, R. O’Reilly Meehan, K. Nolan, and D. B. Murray, “The
dynamics of sliding air bubbles and the effects on surface heat transfer,”
International Journal of Heat and Mass Transfer, vol. 91, pp. 532–542,
2015.
[13] F. Scarano, “Iterative image deformation methods in piv,” Measurement
Science and Technology, vol. 13, no. 1, p. R1, 2002.